Creating a "halo" effect for a material in cycles?
This kind of effect is usually created in post processing.  In Blender's compositor I found that the Filter > Blur node gives a result quite close to what you are looking for, though the Glare node may also work.

Just go the the Node Editor view, switch to compositing nodes, and drop a Blur node in between the Render Layers and Composite nodes.  I found that using Fast Gaussian seems to produce the best looking effect.





To get that even wider glow you can add a second blur node with a much larger blur and mix it with the smaller blur.  Set the mix mode to Add and adjust the Fac slider to suit your tastes.


Click to enlarge.



For the actual mesh I just used the IvyGen technique outlined here with a very strong volumetric emission shader (and no surface shader).